Zara had 189 buttons. ³₇ were yellow and the rest were white and purple. The ratio of the number of white buttons to the number of purple buttons was 1 : 5. Zara decided to buy some more yellow buttons to increase the number of yellow buttons to half of the total number of buttons.

1. How many less white buttons than yellow buttons did he have at first?
2. How many more yellow buttons did he have to buy?

Yellow buttons	White buttons	Purple buttons	Total
3x3	4x3
	1x2	5x2
9 u	2 u	10 u	189

	Yellow buttons	White buttons	Purple buttons
Before	9 u	2 u	10 u
Change	+ ?
After	12 u	12 u
Comparing yellow, white and purple buttons in the end	1	1

(a)
The total number of white buttons and purple buttons is repeated. Make the total number of white buttons and purple buttons the same.  LCM of 4 and 6 is 12.

Total number of buttons at first
= 9 u + 2 u + 10 u
= 21 u

21 u = 189

1 u = 189 ÷ 21 = 9

Number of less white buttons than yellow buttons at first
= 9 u - 2 u
= 7 u
= 7 x 9
= 63

(b)
Number of more yellow buttons that Zara had to buy
= 12 u - 9 u
= 3 u
= 3 x 9
= 27

Answer(s): (a) 63; (b) 27